Abstract Approaches to morphology typically account for regular, completely productive affixation, while ignoring subregular and semiproductive schemata. The alternative approach to derivational morphology presented here relates exceptions and subregularities to productive rules. It accounts for the contribution lexicalized words make to the rule and for the fact that not all new formations follow the 'rules'. It also captures linguistically relevant generalizations that cannot be expressed in other theories. The approach is formalized in terms of complex recursive schemata structured in a multiple inheritance hierarchy, without positing lexical rules or lexical entries for affixes. These schemata structure the existing lexicon, reducing redundancy, and at the same time serve as the basis for productive word formation. The approach handles zero-derivation and other nonconcatenative morphology straightforwardly.